The photograph shows a group of women and children gathering behind a banner, announcing their journey from Land's End to London. The women wear hats and sashes, pavement-skimming skirts, redoubtable expressions; three clutch bicycles, prepared to zoom off. A donkey stands glumly to one side. It looks like a very British day out.

It was much more than that. Natalie McGrath, an Exeter-based playwright, first saw this image in 2008, while leafing through the programme for Her Naked Skin, Rebecca Lenkiewicz's play about the suffragettes (the first play by a woman to be performed on the main stage of the National Theatre). She was immediately intrigued. She started researching the picture, and the event it recorded – a pilgrimage made by the National Union of Women's Suffrage Societies (NUWSS), who were on the non-militant side of the suffrage movement. The pilgrimage started in mid-June 1913, and ended with a mass rally of 50,000 in Hyde Park five weeks later on 26 July. Very little seemed to have been written about it, but trawling through local newspapers, she began to piece the story together.

This was a time of great ferment for the suffrage campaign. Emily Wilding Davison had become a very public martyr for the cause at the start of June, when she was struck by the King's horse Anmer during the Epsom Derby, dying of her injuries four days later. The militants had long been organising outrages up and down the UK – they treated human life as absolutely sacrosanct, but set fire to postboxes and the empty summer houses of the super-rich, and went on major window-smashing expeditions. During this period, for instance, the author Fran Abrams has written: "on two separate days, at a preordained time and with no warning, hundreds of smartly dressed women from Oxford Street to Whitehall, all along Piccadilly and Bond Street, produced hammers from their muffs and laid waste to hundreds of square feet of shop frontage. Emmeline [Pankhurst] was arrested along with a total of 220 other protesters."

Women marching.

The militants were prepared for everything that was thrown at them – eggs, fish and long prison sentences in which they were force-fed, sometimes hundreds of times each. Their campaigns made for excellent newspaper copy. Those on the non-militant side were neither as boisterous, nor as gifted at publicity. But as the Liberal prime minister, Herbert Asquith, continued to mock and obstruct their calls for the vote, they decided to prove just how serious they were.

Fifteen NUWSS volunteers organised eight routes, all over the country, which would end at the rally. (The women marched across England and Wales to London, Scottish suffragists having had their own march from Edinburgh to London in 1912.) The organisers fanned out to the necessary starting points and, after drumming up support, the pilgrimage began. McGrath says it was immediately successful. People would join the march here and there, and by the time the Land's End group moved past Cornwall, "nearly 15,000 men and women had either seen them rally, or walked with them." Over the course of the pilgrimage, 46,000 new signatures were collected in support of the women's vote.

McGrath's play, Oxygen, produced by Dreadnought South West and inspired by that photo, features 18 episodes from the fight for the vote, and has been performed at venues along the original route for the last three weeks, starting with a big send-off at Land's End, exactly 100 years after the campaigners first gathered there. McGrath says women all over the south-west have been celebrating the suffragists. When the theatre company left the Exeter suburb of Topsham, they were seen off from the train station by nearly a hundred women dressed in suffrage outfits – she says the location was chosen because 100 years ago women weren't allowed to stand on rail platforms (they were obliged to sit in the waiting room). Their route will also pass through Wiltshire in the coming weeks, where the original campaigners faced a mob. It was the result of a propaganda campaign by one of the many anti-suffrage groups, who had been visiting locations a week ahead of them to stir up opposition. "In Wiltshire it worked to great effect," says McGrath. "Their van was overturned, there was a riot, and they had to be rescued."

Dreadnought South West's show about the great suffrage pilgrimage.

McGrath isn't the only one to have been inspired by that photograph. Author and activist Lucy-Anne Holmes first saw it last year, and instantly knew she wanted to do something to celebrate the centenary. She therefore set up Walk for Women, a series of walks taking place over the course of this summer – anyone can plan one in their local area and have the details added to the website, so others can join them. There are around 35 planned so far, in locations including Belfast, Glasgow, Cardiff, Barnsley and Manchester – there's even an international one planned, in Paris.

"I just think the mobilisation of 50,000 women, pre-Twitter, pre-Facebook, is remarkable," says Holmes. "I love that powerful collective action." With a new wave of feminism in the UK at the moment, she sees this as a chance for people who have been organising together online to meet in person.

McGrath points out that suffrage campaigners didn't only care about the vote – they were interested in tackling everything from child poverty to sweatshops, and this most basic form of political power was a first step that they could all agree upon and organise around. Holmes is hoping the walks will be a chance for a little utopian thinking, for people to consider what still needs to be tackled in the struggle for equality. "Are we happy with what we're passing on? Can we make things better?"

Last weekend Holmes was at a walk in Newcastle; she hopes to be in Dartmouth this coming Sunday. She is excited about the Woolwich to Greenwich walk, organised by a woman called Faustina, who has written passionately about how she is "walking to tell my fellow black women that everything is possible." Holmes will also be taking part on the most extensive walk, which starts in Brighton on 21 July and will end in Hyde Park on the 27th. There, at 2pm at Speaker's Corner, activists including Laura Bates of Everyday Sexism, and Caroline Criado-Perez of the campaign to keep women on banknotes will speak, 100 years after Millicent Fawcett stood before 50,000 women in a raffia hat, waving her fist.

Holmes started a campaign to end Page 3 almost a year ago now, and says the experience has given her new respect for the suffrage campaigners. "We just tend to think, 'Oh yeah, women won the vote,'" she says, "and we forget about the struggle, and how it took years. Having experienced the resistance and conflict that saying these things brings up, it's not easy. For 50,000 women, doing this will have had a big impact on their lives, and it's great to remember that."

She says some of those who have joined walks so far have seemed to enjoy the rare focus on celebration, rather than protest. "You're not starting with a no, you're starting with a yes. Let's celebrate these women and all they did for our rights and freedom, but also think about the changing role of women over the last 100 years. Those women walked with a dream, to imagine future generations free. Let's do the same."